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Eigenvalue corrector for solving bound states of multichannel Schrödinger equations

✍ Scribed by M.L. Du

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
724 KB
Volume
76
Category
Article
ISSN
0010-4655

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✦ Synopsis

An eigenvalue corrector is given for solving bound states in multichannel Schrodinger equations. Using the renonnalized Numerov method the multichannel equation is integrated from both left and right to the middle. The integrations define an approximate solution which is used to calculate the eigenvalue corrector. The eigenvalue corrector formula is derived from the Newton-Raphson method and accurate to first order in energy. An iterative calculation using the present corrector has the advantages that the starting energy is not required to be close to a true eigenvalue and that the convergence rate is quadratic. The theory is illustrated using a model two-channel eigenvalue problem. The results obtained here for the multichannel case are generalizations of those obtained by Cooley for the one-channel case. When the present iterative method is combined with the node counting method for locating the energy interval of a desired level, it provides a very powerful method for solving multichannel eigenvalue problems.

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